1. Field of the Invention
The present invention relates generally to statistical signal processing and its application to imaging, and more particularly to a method and/or associated apparatus for independent component imaging from mixed observations.
2. Description of the Prior Art
Spotted cDNA microarrays promise powerful new tools for the large-scale analysis of gene expression. Using this technology, the relative mRNA expression levels derived from tissue samples may be assayed for thousands of genes simultaneously. Such global views are likely to reveal previously unrecognized patterns of gene regulation and generate new hypotheses warranting further study as shown by J. Khan, J. S. Wei, M. Ringner, L. H. Saal, M. Lananyi, F. Westermann, F. Berthold, M. Schwab, C. R. Antonescu, C. Peterson, and P. S. Meltzer, xe2x80x9cClassification and diagnostic prediction of cancers using gene expression profiling and artificial neural networks,xe2x80x9d Nature Medicine, vol. 7, no. 6, pp. 673-679, June 2000 [hereinafter Khan et al.]; and T. R. Golub, D. K. Slonim, P. Tamayo, C. Huard, M. Gaasenbeek, J. P. Mesirov, H. Coller, M. L. Loh, J. R. Downing, M. A. Caligiuri, C. D. Bloomfield, and E. S. Lander, xe2x80x9cMolecular classification of cancer: class discovery and class prediction by gene expression monitoring,xe2x80x9d Science, vol. 286, pp. 531-537, October 1999 [hereinafter Golub et al.], the entire contents and disclosures of which are hereby incorporated by reference herein. On the other hand, remarkable advances have been made in developing molecular-targeted contrast agents, ligands and imaging probes. Such imaging capabilities may allow for the visualization and elucidation of important disease-causing physiologic and molecular processes in living tissue, as shown by Z. Szabo, P. F. Kao, W. B. Mathews, H. T. Ravert, J. L. Musachio, U. Scheffel, and R. F. Dannals, xe2x80x9cPositron emission tomography of 5HT reuptake sites in the human brain with C11McN5652 extraction of characteristic images by artificial neural network analysis,xe2x80x9d Behavioural Brain Research, vol. 73, pp. 221-224, 1996 [hereinafter Szabo et al.]; as well as L. Cinotti, J. P. Bazin, R. DiPaola, H. Susskind, and A. B. Brill, xe2x80x9cProcessing of Xe127 regional pulmonary ventilation by factor analysis and compartmental modeling,xe2x80x9d IEEE Trans. Med. Imaging, vol. 10, no. 3, pp. 437-444 (1991), the entire contents and disclosures of which are hereby incorporated by reference herein.
One of the major bottlenecks in molecular imaging is the ability to make sense of and interpret information derived from clinical-setting sources. For example, in the case of solid tumors, one of the challenges is the partial volume effect, i.e., the heterogeneity within the tumor samples caused by stromal contamination, as shown in Khan et al. and Golub et al. Blind application of microarray expression and data analysis could result in extracting signatures reflecting the proportion of stromal contamination in the sample, rather than underlying tumor biology. Effective computational tools that exclude gene expressions in stromal cells are highly desirable. In addition, imaging neurotransporters in the brain requires the passage of radioligands across the blood brain barrier with high lipophilicity. But lipophilicity carries the risk of high nonspecific binding and retention in the white matter and may result in a bias of the estimated kinetic parameters that are used to measure binding to specific recognition sites, as shown by Szabo et al. Separation of the mixed bindings is important for finding the true distribution of specific binding sites in comparative studies.
There exist algorithmic methodologies that include, for example, Independent Component Analysis (ICA), which is primarily a mathematical theory, and a FastICA algorithm, which is a neural network implementation of the ICA principles that are publicly available, as well as several modifications to these methodologies. However, the applications of ICA/FastICA techniques to real-world problems are limited. The fundamental methodologies suffer from key restrictions, such as that the underlying sources must be completely statistically and mutually independent with nongaussian distributions, which is hard to accomplish in most real-world situations. Thus, there is a need for improvement of ICA methodology with regard to such restrictions and for enlarged applications of such improved technology to independent component imaging.
It is therefore an object of the present invention to provide a statistically-principled neural computation approach/algorithm to partial independent component analysis.
It is a further object of the present invention to provide such a partial independent component analysis approach to independent component imaging.
It is a further object of the present invention to provide an apparatus for conducting a partial independent component analysis for independent component imaging.
It is a further object of the present invention to provide an index selection method and apparatus to identify an index subspace defining the observations of the sources such that over such index subspace, the source signals/images are independent, or at least more independent than the original signals/images.
It is a further object of the present invention to provide an index selection method and apparatus to identify an index subspace defining the observations of the sources such that over such index subspace, the source signals/images are nongaussian, or at least less gaussian than the original signals/images.
It is a further object of the present invention to provide a linear and/or nonlinear regression/correlation analysis over a scatter plot (i.e., joint distribution of the source samples) to measure the contributions of each index to the independence between the sources and/or nongaussianities.
It is a further object of the present invention to provide an apparatus for conducting linear and/or nonlinear regression/correlation analysis over a scatter plot (i.e., joint distribution of the source samples) to measure the contributions of each index to the independence between the sources and/or nongaussianities.
It is a further object of the present invention to provide a linear and/or nonlinear regression/correlation analysis through weighted Fisher criterion based cluster analysis (i.e., separability) to measure the contributions of each index to the independence between the sources using multiple realizations.
It is a further object of the present invention to provide an apparatus for conducting a linear and/or nonlinear regression/correlation analysis through weighted Fisher criterion based cluster analysis (i.e., separability) to measure the contributions of each index to the independence between the sources using multiple realizations.
It is a further object of the present invention to provide an iterative normalization method and apparatus that may solve the ambiguity problems associated with conventional ICA (i.e., resealing and permutation).
It is a further object of the present invention to apply ICA and/or PICA methods to partial volume correction in microarray expression studies (mRNA and protein).
It is a further object of the present invention to apply ICA and/or PICA methods to binding separation in dynamic positron emission tomography studies.
It is a further object of the present invention to apply ICA and/or PICA methods to binding separation in receptor imaging by positron emission tomography and magnetic resonance imaging where single or multiple imaging probes are used.
It is a further object of the present invention to apply ICA and/or PICA methods to signal separation in gene expression imaging by positron emission tomography and optical imaging where single or multiple imaging probes are used.
It is a further object of the present invention to apply ICA and/or PICA methods to signal separation in anatomic imaging by multiple energy x-ray and/or by multi-spectrum projective ultrasound.
It is a further object of the present invention to apply ICA and/or PICA methods to fundamental factor extraction in gene regulation studies (i.e., regulatory network, pathway discovery) based on time course gene expressions.
It is a further object of the present invention to apply ICA and/or PICA methods to change detection and analysis in existing and future imaging studies where the images of the same subject are taken over a period of time.
It is a further object of the present invention to apply ICA and/or PICA methods to signal separation in existing and future anatomic, function, and molecular imaging where the detected signals are the mixture of several underlying sources.
According to a first broad aspect of the present invention, a method for analyzing images is provided comprising the steps of acquiring a digital image of an observation, the digital image being observation data; vectorizing the observation data to generate an observation vector x(i); determining a de-mixing matrix W; determining an output vector y(i)=Wx(i); recovering a source vector S(i), where S(i)=y(i); and utilizing the source vector S(i) to analyze the image.
According to a second broad aspect of the present invention, an apparatus for analyzing images is provided comprising means for acquiring a digital image of an observation, the digital image being observation data; means for vectorizing the observation data to generate an observation vector x(i); means for determining a de-mixing matrix W; means for determining an output vector y(i)=Wx(i); means for recovering a source vector S(i), where S(i)=y(i); and means for utilizing the source vector S(i) to analyze the image.
According to a third broad aspect of the present invention, an apparatus for analyzing images is provided comprising (A) means for acquiring a digital image of an observation, the data image being observation data; (B) means for vectorizing the observation data to generate an observation vector x(i); (C) means for determining a de-mixing matrix W, wherein said de-mixing matrix is determined by using an apparatus comprising (1) means for centering observation data to make its mean zero and where C=E[xxT]; (2) means for choosing an initial demixing matrix W; (3) means for computing y=Wx, xcex2k=xe2x88x92E[ykg(yk)], xcex1k=xe2x88x92(xcex2k+E[gxe2x80x2(yk)])xe2x88x921, for k=1, . . . , m (4) means for updating W by W+diag(xcex1k)(diag(xcex2k)+E[(g)(y)(y)T])W; and (5) means for decorrelating and normalizing by W←(WCWT)xe2x88x921/2W; (D) means for determining an output vector y(i)=Wx(i), wherein said output vector is determined by an apparatus comprising (1) means for estimating y(j)=W(j)x by FastICA over F for j=0; (2) means for identifying index subspace I according to:             "LeftBracketingBar"                                                  ay              1                        ⁡                          (              i              )                                                          y              2                        ⁡                          (              i              )                                      -        1            "RightBracketingBar"        ≥    ε    ,                    where        ⁢                  xe2x80x83                ⁢        a            =                        ∑                      i            =            1                    d                ⁢                                                            y                1                            ⁡                              (                i                )                                                                    y                2                            ⁡                              (                i                )                                              /                                    ∑                              i                =                1                            d                        ⁢                                                                                y                    1                                    ⁡                                      (                    i                    )                                                  2                                                                                                        y                      2                                        ⁡                                          (                      i                      )                                                        2                                xe2x80x2                                                          ;  
(3) means for estimating y(i+1)=W(j+1)y(j) by FastICA over I; and (4) means for computing y(i+1)=W(j+1)y(j) over Fxe2x88x92I; (E) means for recovering a source vector S(i), where S(i)=y(∞); and (F) means for utilizing the source vector S(i) to analyze the image.
Other objects and features of the present invention will be apparent from the following detailed description of the preferred embodiment.